Asymptotic minimaxity in the change-point problem
Andrew L. Rukhin · Lecture notes-monograph series · 1994
A lower bound on the limit of the minimax risk under the zero-one loss function is established in the classical setting of the change-point estimation problem.This bound is attained by the maximum likelihood estimator in the situation when the two probability distributions before and after the change point are completely known.The nature of this bound is related to the multiple decision problem and a variety of inequalities relating it to the information-type measures is deduced.Minimaxity of the maximum likelihood procedure is proved for normal observations with unknown means.